Flow equivalence of G-SFTs
Mike Boyle, Toke Meier Carlsen, Søren Eilers · Transactions of the American Mathematical Society · 2019
In this paper, a G G -shift of finite type ( G G -SFT) is a shift of finite type together with a free continuous shift-commuting action by a finite group G G . We reduce the classification of G G -SFTs up to equivariant flow equivalence to an algebraic classification of a class of poset-blocked matrices over the integral group ring of G G . For a special case of two irreducible components with G = Z 2 G=\mathbb {Z}_2 , we compute explicit complete invariants. We relate our matrix structures to the Adler-Kitchens-Marcus group actions approach. We give examples of G G -SFT applications, including a new connection to involutions of cellular automata.